Sentence examples for a class of functions from inspiring English sources

The phrase "a class of functions" is correct and usable in written English.
It can be used in mathematical or programming contexts to refer to a group of functions that share common characteristics or behaviors.
Example: "In calculus, we often study a class of functions known as polynomials, which have specific properties and applications."
Alternatives: "a category of functions" or "a type of functions".

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The aim of this paper is to construct a functional calculus defined on a class of functions two variables and satisfying natural properties (linearity and multiplicativity modulo the trace class).

In this paper, we will apply the fixed point method to prove the Hyers-Ulam-Rassias stability of the functional equation (1.2) for a class of functions of a vector space into a Banach space.

To improve the accuracy, the functional risk R(w) should be minimized over a class of functions f (x, w), w ∈ W.

The construction of linear underestimators for a class of functions is also presented.

For non-linear objective functions, we follow a geometry-based approach to design approximation algorithms for a class of functions fulfilling certain conditions.

This enables us to seek for the optimum in a class of functions and their derivatives instead of a class of shapes.

Extension of such constructions beyond the simple case has also been shown to be possible, provided the concept of a random variable can be extended to a class of functions that are more general than the measure-theoretic class.

A numerical experiment for a class of functions in known Sobolev smoothness classes gives L2 errors for the fully discrete needlet approximation that are almost identical to those for the original semidiscrete needlet approximation.

To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free.

This paper analyzes then-fold composition of a non-linear integral operator acting on a class of functions on [0, ∞). Attracting orbits and attracting fixed points are identified. Various results of convergence to these orbits and to these fixed points are derived. The proofs are based on order-preserving properties and comparison techniques.

Finally, with an eye to finding a class of functions whose integral interacts well with differentiation, we give sufficient conditions that guarantee the fulfillment of the fundamental theorem of calculus, and prove the Lebesgue differentiation theorem for the integral in the sense of Vogt.

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